Mid-infrared (mid-IR) light with wavelengths ranging from 2 μm to 30 μm have unique capabilities of fingerprinting chemicals via their characteristic absorption spectra (see, e.g., Refs. [1] and [2]) and propagating over longer distances in scattering media compared to light with shorter wavelengths (see, e.g., Refs. [3] and [4]). As a result, mid-IR light is uniquely positioned to address a number of important issues in our security, health, and environment (see, e.g., Refs. [5]-[9]). Recently, there has been a rapid development in mid-IR sources and detection systems (see, e.g., Refs. [10]-[13]). However, despite prevalent civil and military interests in high-performance mid-IR modulators and spatial light modulators (SLMs), a viable path towards realizing such devices remains elusive. Existing approaches to modulate mid-IR light have a number of drawbacks that limit their applications. For example, mid-IR modulators based on acousto-optic effects are bulky, require high operating voltage, and have limited modulation speed (see, e.g., Ref [14]). Modulators based on quantum confined Stark shift of inter-subband transitions in semiconductor quantum wells require sophisticated material growth and it is hard to realize pure-phase modulation because of the high absorption losses associated with inter-subband transitions (see, e.g., Refs. [15]-[17]). Active optical components for controlling mid-IR radiation thus present a bottleneck in the development of mid-IR science and technology.
Graphene can be used as the active medium because of its largely tunable optical conductivity in the mid-IR (see, e.g., Refs. [18]-[20]). Metallic plasmonic antennas demonstrate a strong interaction between graphene and infrared light so that the material perturbation introduced by graphene leads to large changes in the optical response of the antennas (see, e.g., Refs. [21] and [22]). Modulators and SLMs consisting of arrays of such antennas can have the following distinguishing features. First, they are optically-thin planar devices. The thickness of the active antenna arrays is less than a few percent of the free-space wavelength. Abrupt and controllable changes to the intensity and phase of light are achieved through optical scattering at plasmonic antennas (see, e.g., Ref. [23]) instead of through an accumulative effect via propagation. Second, our flat optical components can mold optical wavefronts with high spatial resolution and with fast modulation rate because the tunable plasmonic antennas have sub-wavelength footprints and small RC time constant. Previous planar infrared and microwave components have shown static optical responses (see, e.g., Refs. [24]-[33]).
A composite structure consisting of plasmonic antennas and graphene can have widely tunable antenna resonances and, as such, can be used as a building block for reconfigurable flat optical components. This is based on several principles or observations. First, graphene has widely tunable optical conductivity in the mid-IR. The doping of graphene can be adjusted using a bias voltage by a factor of ˜10 at room temperature (see, e.g., Ref [34]), which leads to a large change in its sheet conductivity a and therefore the in-plane electric permittivity ε81=1+iσ/(εoωt), where εo is the vacuum permittivity, ω is angular frequency, and t is the thickness of graphene. This effect is illustrated in FIGS. 1(a) and 1(b), which show exemplary in-plane electric permittivity (ε∥) of graphene at different doping levels at room temperature. Solid and dashed lines represent real and imaginary components, respectively. Second, metallic plasmonic antennas are able to capture light from free space and concentrate optical energy into sub-wavelength spots with intensity a few orders of magnitude larger than that of the incident light (see, e.g., Refs. [21]-[22]). Third, by placing graphene in the hot spots created by plasmonic antennas and by tuning the optical conductivity of graphene, the resonant frequency of the metallic plasmonic antennas is tunable over a wide range.
According to perturbation theory, the change in resonant frequency ωres of a system caused by material perturbation is given by equation (1) below (see, e.g., Ref [35]),
                                                        ω              res                        -                          ω              o                                            ω            o                          ≈                              -                          ∫                              ∫                                                      ∫                    V                                    ⁢                                      d                    ⁢                                                                                  ⁢                                          V                      ⁡                                              [                                                                                                            (                                                              Δ                                ⁢                                                                                                      μ                                    ↔                                                                    ·                                                                      H                                    →                                                                                                                              )                                                        ·                                                                                          H                                →                                                            o                              *                                                                                +                                                                                    (                                                              Δ                                ⁢                                                                                                      ɛ                                    ↔                                                                    ·                                                                      E                                    →                                                                                                                              )                                                        ·                                                                                          E                                →                                                            o                              *                                                                                                      ]                                                                                                                                      ∫                          ∫                                                ∫                  V                                ⁢                                  d                  ⁢                                                                          ⁢                                      V                    ⁡                                          (                                              μ                        |                                                                              H                            →                                                    o                                                ⁢                                                  |                          2                                                ⁢                                                  +                          ɛ                                                |                                                                              E                            →                                                    o                                                ⁢                                                  |                          2                                                                    )                                                                                                                              (        1        )            where the denominator represents the unperturbed total energy and the numerator represents the change in magnetic and electric energies, Δ and Δ respectively, caused by the material perturbation (in tensor format to account for anisotropy); {right arrow over (E)} and {right arrow over (H)} are electric and magnetic fields, respectively, in the presence of the material perturbation; {right arrow over (E)}o and {right arrow over (H)}o are the respective unperturbed fields; and {right arrow over (E)}*o and {right arrow over (H)}*o are their respective complex conjugates. According to the theory expressed by equation (1), a large tuning in ωres can be achieved by enhancing the overlap between the perturbation material (e.g., graphene) and a strong optical field, Δ·{right arrow over (E)}. Since optical resonances are associated with large changes in the amplitude and phase of the scattered light (see, e.g., Ref [23]), the large tuning in ωres can produce significant intensity, phase, and polarization modulation.
Although graphene is one material that exhibits advantageous properties when combined with metal in a plasmonic antenna, the person of ordinary skill will readily understand that graphene is merely exemplary and many other such materials may be used advantageously. For example, thin-film materials such as vanadium dioxide, boron nitride, and molybdenum disulfide may be combined with metal in a plasmonic antenna.
Thus, it may be beneficial to provide a plasmonic antenna (e.g., graphene-metal plasmonic antenna) that efficiently modulates the intensity, phase, and/or polarization of radiation (e.g., mid-IR radiation) that can address and/or overcome at least some of the issues and/or problems described herein above.